VISUALIZATION OF THE STABILITY AREA OF THE CAUCHY DIFFERENCE PROBLEM IN THE COMPLEX PLANE - Bektemessov, М.А.; Kabanikhin, С.И.; Kuryshbayev, Е.Ж. (Bulletin of Abai KazNPU. Series of Physical and Mathematical sciences, 2022)
The article considers the possibility of obtaining fractal images, which forms by calculating the relative error of various finite-difference schemes for solving the Cauchy problem using iterative processes. The constructed graphical algorithm made it possible to simulate the image of the set for study, for example, to identify areas of stability for solving the problem. When considering the connection between fractals and the correctness of problems of mathematical physics, the authors found that, with a certain digital coding, the distribution of the relative error gives a bizarre repetitive image and self-similarity. The resulting model allows you to determine the nature of the changes in the set depending on the initial parameters, such as step, accuracy, boundaries of the complex plane. A computer graphical analysis of these phenomena is given. The computer can be turned into a kind of microscope and use it to observe the behavior of the boundaries of the region.